This invention relates to a calculating device for determining odds in a pari-mutuel wagering system. More particularly, this invention relates to a calculating device and a mechanical method for calculating win, place and show odds for events, such as horse races, having pari-mutuel wagering systems. Still more particularly, this invention relates to a mechanical method and calculating apparatus for calculating quickly the potential profit per dollar wagered for win, place and show bets by utilizing a knowledge of the amounts previously wagered on the contest.
By way of background, the three winning positions in a horse race are generally referred to as the "win" position (first), the "place" position (second), and the "show" position (third). The return on wagering for each position is determined from a number of factors and is important in determining on which horse and for what position a potentially profitable wager should be placed. For example, in wagering on the win position, the total amount of money in the win pool, i.e., the money wagered on entrants to win the contest, less a mutuel take from the pool which goes to the track and State, is available to return to holders of win tickets on the horse finishing in the win position. The pool profit is the returnable dollars minus the amount wagered on the winning entrant or winning entrants. The win odds, or the profit per dollar wagered on the winning entrant, is obtained by dividing the pool profit by the amount wagered on the winning entrant. The odds plus one, multiplied by the actual dollars wagered by a person on the winning entrant, provides the actual payoff for the winning wager to that person.
However, the calculations to determine the profit per dollar wagered to holders of redeemable place or show bets is more complicated. In wagering on the place position, the bettors entitled to share in the place pool are those who have wagered on the horses that finish in the win position or the place position. Thus, the amount wagered in the place pool on the horse that came in first and the amount wagered on the horse that came in second share the potential profit of the place pool. Similarly, the potential profit from the show pool is shared by the bettors who have wagered on the horses which came in first, second and third.
At a racetrack, the amount wagered on a particular horse in the win pool, the place pool and the show pool are generally illustrated, as are the total amounts in each of the respective pools. Moreover, the win odds for each horse are generally shown, although somewhat imprecisely since the odds value approximate the true value. However, it is a problem at a racetrack to evaluate quickly the likely place odds or show odds as well as the win odds with greater precision than that shown on the tote board. Occasionally, due to disproportionate amounts wagered on the entrants in the different pools a horse may pay as much or more to place or show as to win or pay as much or more to show as to place. Thus, an immediate knowledge of win, place and show odds, not now generally available, is important information for wagering decisions in parti-mutuel systems.
At racetracks with pari-mutuel wagering on horse racing, for example, the approximate win odds are provided on a tote board. However, for place and show wagering, the only data generally readily available are the amounts wagered on each horse for each pool and each wagering pool total. To obtain the place or show odds of a wager, a person must use that wagering data in a complex calculation shown below.
The calculation to obtain the place or show odds is as follows: ##EQU1## where: x = the share of the pool profit awarded to the bet, the odds of which are being calculated, and, specifically, at United States tracks, x = 1/2 for place and 1/3 for show;
p = the total amount in either the place or the show pool, depending on whether the place or show odds are being calculated; PA1 t = the amount withheld as a mutuel take, or track take, where t is about 0.16p at United States tracks or 16% of the total wagers in the pool; PA1 a = amount wagered on the bet, the odds of which are being calculated; and PA1 b = amount wagered on the other bet sharing the place pool profits or the amount wagered on the other two bets sharing the show pool profits.
It can be seen that the odds are influenced by the amount wagered on the other pool-sharing bets designated by "b" in Eq. 1. In a field of N horses, there are N-1 possible payoff combinations with the other place qualifying horse for each horse to place. For the show pool, there are [(N-2) + (N-3) + ...1] possible payoff combinations with the two other show qualifying horses for each horse to show. The place or show odds of a horse for any combination is found by inserting the appropriate value of "b" into the equation.
The method and apparatus of this invention can be advantageously used for quickly calculating the minimum place or show odds by using the maximum value of b, or for relatively precisely calculating win, place or show odds without resort to the tedious use of the equation above. Adding to the possible calculative workload is the periodic updating of the wagering amounts provided on the tote board, which makes repetitive calculation desirable.
Still another factor in influencing the odds is the mutuel take t which generally will vary from State to State. For this reason, a method for taking into account this variable mutuel take factor is also desirable.
In view of the value of knowing place and show odds, the number of possible payoff combinations which may be calculated, and the periodic updating of data, it is a principle object of this invention to provide by a simple mechanical calculation on an easily usable calculator the place or show odds of a bet for whatever combination of horses the wagerer desires.
It is another general object to provide for obtaining many possible payoff combinations of a bet with a minimum amount of readjustment on an odds calculator.
It is another object of this invention to provide for updating wagering data with a minimum amount of readjustment on an odds calculator.
It is another purpose of this invention to provide win odds of greater precision than are generally provided on the tote board at a racetrack.
It is still another object of this invention to enable odds calculations for different percentages of tax-track mutuel take.
An improved understanding and other objects and purposes of the invention will be apparent from reading the following detailed description of the invention and the accompanying drawings.